Hi,

I have a very simple induction problem that i'd like help solving.

Prove that for all positive Integers n, that :

I know that the first step is to replace n with n+1 but then what?

/Jones

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- September 28th 2008, 01:01 PMJonesSimple induction help
Hi,

I have a very simple induction problem that i'd like help solving.

Prove that for all positive Integers n, that :

I know that the first step is to replace n with n+1 but then what?

/Jones - September 28th 2008, 01:07 PMMoo
Hello,

The first step is to prove it is true for n=1.

The second step is to state the inductive hypothesis, that is to say assuming that

The third step is to prove that it is true if you "replace" n by n+1, that is to say :

Now, use the inductive hypothesis to substitute

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Another way would have been to note that and use telescoping series (Telescoping series - Wikipedia, the free encyclopedia) - September 29th 2008, 03:09 AMJones
Hmm, how do you mean?

isn't it just a simple matter of:

- September 29th 2008, 07:29 AMShowcase_22
I'd do it like this:

Proving it true for n=1:

True for n=1.

That's the easy bit. I'll leave it up to you to do the rest.